### Video Transcript

Elizabeth and Olivia are saving
their allowances. Elizabeth has 100 dollars in her
account and saves 10 dollars per month. Olivia has 50 dollars in her
account and saves 15 dollars per month. Write an equation that can be used
to find π, the number of months until their accounts have the same balance.

Letβs firstly consider what we know
about Elizabeth. She has 100 dollars in her account
and saves 10 dollars per month. This means that an expression for
the total amount of money she has in her account is 100 plus 10 multiplied by π,
where π is the number of months that she has been saving. Olivia, on the other hand, has 50
dollars in her account and saves 15 dollars per month. The expression for the amount of
money in Oliviaβs account after π months is 50 plus 15 multiplied by π.

We want to write an equation where
both girls have the same balance. Therefore, the two expressions need
to be equal. 100 plus 10π has to be equal to 50
plus 15π. This equation can be used to find
π, the number of months until the accounts have the same balance. Whilst we have not been asked to
solve the equation in this case, we can do so using a few steps.

Firstly, we can subtract 50 from
both sides of the equation. 100 minus 50 is equal to 50. Therefore, the left-hand side
simplifies to 50 plus 10π. Subtracting 50 from the right-hand
side leaves us with just 15π. Our next step is to subtract 10π
from both sides of this new equation. On the left-hand side, the 10 πs
would cancel, leaving us with 50. 15π minus 10π is equal to five
π. Therefore, the equation simplifies
to 50 is equal to five π.

Our final step is to divide both
sides of this equation by five. 50 divided by five is equal to
10. And, five π divided by five is
just equal to π. This means that the solution to the
equation, 100 plus 10π is equal to 50 plus 15π, is π equals 10. We can therefore conclude that
after 10 months, the girls will have the same balance. Elizabeth would have 100 dollars
plus 10 multiplied by 10 dollars. This is equal to 200 dollars. Olivia would have 50 dollars plus
10 multiplied by 15 dollars. This is also equal to 200
dollars. Therefore, our answer is
correct.